Roberto Mancini is confident Manchester City will retain the title if they travel to Manchester United in April within "four or five points" of their hosts after his team responded impressively to the leaders' 2-1 victory over Liverpool earlier on Sunday to register a first league win at Arsenal since 1975.

The Italian was pleased with his side's reaction to slipping briefly 10 points behind Sir Alex Ferguson's team, with his mood darkened only by the red card awarded to Vincent Kompany late on. City will appeal against the dismissal, claiming the Belgian's challenge on Jack Wilshere was not two-footed but, regardless, have been heartened by this comfortable success against opponents who had been reduced to 10 themselves early on.

"It was an important victory because it's difficult to play and win here," said Mancini. "United are a really strong team. In this moment they play very well. But the season is long. It's important for us to be there, close with them, and we will arrive the moment they lose points. We're under pressure maybe but everything can change.

"We have the derby on 6 April and we need to arrive there five or four points behind; it is OK. We know that we are behind. I don't think that we deserve to stay seven points behind United but that is where we are. We need to play well, that is all we can do, we need to work strong if we want to have a chance at the end."

The City manager's frustration was reserved for Mike Dean's decision to send off Kompany 15 minutes from time after the centre-half stretched into a tackle on Wilshere. The official interpreted the Belgian's challenge as two-footed from where he viewed it – the player's right foot was actually tucked slightly behind his left calf as his left won the ball cleanly – with Kompany later posting a picture of the tackle on his Twitter account.

"No grudges against the referee, I understand the difficulty of the job," he wrote. "About the tackle: if the ball is overrun by the opponent and a 50/50 challenge occurs, collision is inevitable. Ultimately I'm a defender. Appeal may work or not. I will never pull out of a challenge, as much as I will never intend to injure a player." If the card stands, Kompany will miss the FA Cup fourth-round tie against Stoke or Crystal Palace and league games against Queens Park Rangers and Fulham.

"He went into the tackle, anticipating the opponent and took the ball," said Mancini. "I don't know how it is possible to get a red card like this. It was no foul, no red card. We will appeal, because it is impossible that we can lose one player for three games for nothing. I am 48 but I can see it very well and [his right foot] was a minimum of 50cm from the opponent. The referee made a mistake."

Arsène Wenger suggested his side had lacked conviction in the early stages, their nervous opening compounded by Laurent Koscielny's 10th-minute dismissal for hauling down Edin Dzeko. "You have to live with that decision but, overall, we started too timid with not enough authority," said the Arsenal manager. "We allowed them to dictate. You have to impose your own personality, especially defensively, and we did not do that. It's frustrating because the team showed great heart and desire after that but we're a bit too nervous to play in a serene way at home and that is costing us."

City took advantage with a first league win at Arsenal for more than 37 years, fine reward for those City fans win rewarded their fans who had paid £62 a ticket to attend. The visitors had returned 912 of their allocation of 3,000 to Arsenal, with the assistant referee John Brooks urging Joe Hart and Joleon Lescott at the final whistle to "go and thank them, they've paid £62". The Premier League's chief executive, Richard Scudamore, had admitted earlier in the day that he did not blame City's fans for not taking up their full allocation.